Competitive exploration of rectilinear polygons

Exploring a polygon with robots when the robots do not have knowledge of the surroundings can be viewed as an online problem. Typical for online problems is that decisions must be made based on past events without complete information about the future. In our case the robots do not have complete information about the environment. Competitive analysis can be used to measure the performance of methods solving online problems. The competitive ratio of such a method is the ratio between the method's performance and the performance of the best method having full knowledge of the future. We prove constant competitive strategies and lower bounds for exploring a simple rectilinear polygon in the L1 metric.